Fixed point theorems for \(\psi\)-contractive mappings in ordered metric spaces. (English) Zbl 1235.54027

Summary: We obtain some new fixed point theorems for \(\psi\)-contractive mappings in ordered metric spaces. Our results generalize or improve many recent fixed point theorems in the literature (e.g., J. Harjani, B. López and K. Sadarangani [Abstr. Appl. Anal. 2010, Article ID 190701 (2010; Zbl 1203.54041); Comput. Math. Appl. 61, No. 4, 790–796 (2011; Zbl 1217.54046)]).


54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54E50 Complete metric spaces
54E40 Special maps on metric spaces
Full Text: DOI


[1] S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integerales,” Fundamenta Mathematicae, vol. 3, pp. 133-181, 1922.
[2] L. B. Ćirić, “A generalization of Banach’s contraction principle,” Proceedings of the American Mathematical Society, vol. 45, no. 2, pp. 267-273, 1974. · Zbl 0291.54056 · doi:10.2307/2040075
[3] S. K. Chatterjea, “Fixed-point theorems,” Comptes Rendus de l’Académie Bulgare des Sciences, vol. 25, pp. 727-730, 1972. · Zbl 0274.54033
[4] B. S. Choudhury, “Unique fixed point theorem for weakly C-contractive mappings,” Kathmandu University Journal of Scinece, Engineering and Technology, vol. 5, no. 1, pp. 6-13, 2009.
[5] J. Harjani, B. López, and K. Sadarangani, “Fixed point theorems for weakly C-contractive mappings in ordered metric spaces,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 790-796, 2011. · Zbl 1217.54046 · doi:10.1016/j.camwa.2010.12.027
[6] J. Harjani, B. López, and K. Sadarangani, “A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space,” Abstract and Applied Analysis, vol. 2010, Article ID 190701, 8 pages, 2010. · Zbl 1203.54041 · doi:10.1155/2010/190701
[7] J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223-239, 2005. · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[8] A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 1435-1443, 2004. · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.